The morning after conducting the Rotterdam Philharmonic Orchestra in Mahler's Ninth Symphony – among the most gruelling symphonies ever written – Yannick Nézet-Séguin looks as if he could even now go a few rounds with Amir Khan and come out unscathed. "If there's one gift I have from nature," says the diminutive 34-year-old French-Canadian in his Québécois-accented English, "it's a sort of limitless energy. I always find more – I don't know how."

It's just as well he's got those endless energy reserves: in a couple of hours, he has to get on the podium again to lead the Rotterdam Philharmonic in another performance of Mahler's Ninth, the fourth in as many days of this epic symphony. "Four in a row – that's a lot for such a piece. But who can complain? It's so wonderful to live with this music – but it is indeed like dying and resurrecting every night."

Nézet-Séguin will be in the UK next week to conduct another of the giants of late romantic repertoire, Bruckner's Eighth Symphony, with the London Philharmonic, where he is principal guest conductor. He will also make his debut with the Orchestra of the Age of Enlightenment, conducting an all-Haydn programme. It's easy to understand why orchestras around the world want to snap him up. Nézet-Séguin is 34, but his music-making has maturity and intelligence. Last May he won the prestigious RPS Young Artist of the Year award.

In the Mahler in Rotterdam, what impressed wasn't so much the massive climaxes or the bold colours, but rather how Nézet-Séguin created a single narrative from the contrasts between all four movements. "The line between each of the movements is not obvious in this symphony," he tells me, "and the first movement's structure is so difficult, and so forward-thinking, -looking and -sounding. What I wanted to do was to infuse a sort of intellectual overview of the piece with my own warmth, but at the same time really respect what Mahler wrote." It worked: audience members I spoke to preferred Nézet-Séguin's way with this symphony to Valery Gergiev's, his predecessor in Rotterdam. One Dutch reviewer called the performance "perfect".

On the face of it, Nézet-Séguin's journey to these sorts of interpretative heights has been astonishingly serene. Growing up in Montreal, he was 10 when he decided to become a conductor. He started waving the baton at his cathedral choir, then studied piano at the conservatoire in Montreal and was mentored by Carlo Maria Giulini, the great Italian conductor.

I tell Nézet-Séguin that I've found some YouTube footage of him as a schoolkid showing off his conducting skills to his classmates, performing some impressive karaoke-conducting to a recording of Ravel's Boléro. Even now, he uses some of the same gestures: the big, swooping arcs of his arms, and the intensity of his facial expressions.

"I'm not sure it's a good thing that my technique is similar now to what it was then!" he laughs. "The funny thing is that when you're that young, you dream of something without really knowing what it implies. But, on my way to becoming a conductor, I haven't had many surprises. I had a dream, and that dream has come true, and there is something normal about it, in a way."

Normal – really? To have had your own orchestra (the Orchestre Métropolitain du Grand Montréal) since the age of 24, and to be one of the world's most in-demand maestros when you've scarcely turned 30? "Well, no, there's nothing normal about it in that sense," he concedes. "This morning, I was thinking, 'Oh my God, what a surreal life, to go through all these emotions, to have all this responsibility, and to get the biggest spiritual food with this music.' It's a hyper-life, definitely. But I'm still very connected to the 10-year-old who made that decision to be a conductor."

Nézet-Séguin's relationship with his guru, Giulini, was uniquely close. "He remains completely special for me. He used to say that conductors were 'luggage and transit'. That was their function: the composers need their masterpieces to be carried and brought to people, so that's what we're doing. It's about not taking yourself too seriously."

There's a Giulini connection in his choice of repertoire, too, especially the former's beloved Bruckner. Few young conductors feel an affinity with the visionary music of the 19th century's most devoutly religious symphonist, not least because his music isn't flashy enough to make a reputation. But Nézet-Séguin felt a spiritual connection with Bruckner from the start. "The first symphony of his I performed was the Ninth, with Montréal. I must have been 26. And I felt so strangely at ease with this music. When I left the stage, I said to my parents and close friends, 'It's strange, I feel I've conducted that before.' He is the only composer with whom I've had this feeling.

"Of course, my Bruckner will develop, but you need to start young," he continues. "Just because a good wine takes a long time to mature, doesn't mean you shouldn't drink it when it's younger. I'm conscious that a 30-year-old's Bruckner is different from a 60-year-old's, but I can give a different point of view on the music. With the London Philharmonic, I'm aware of the great Bruckner they have produced with Klaus Tennstedt and Kurt Masur, so when I go there, I feel I'm just carrying their tradition, giving it my own little touch. I'm not trying to reinvent the wheel – I'm just trying to share my love and respect for this music with others."

Nézet-Séguin's level-headedness and optimism make him well equipped for the life of an itinerant maestro; he says he relishes the loneliness of studying music and accepts the constrictions on his social life. "More and more, I make my parents travel with me, so that I feel surrounded and supported – but in every city I have friends. I could have decided very early on not to travel, just to stay in Montreal, but I want this life, and I want to enhance what's good about it." And why not? With debuts coming up with the Philharmonics of Vienna and Berlin, and annual trips to the Metropolitan Opera in New York, Nézet-Séguin's rise looks assured.

Before he leaves for another date with Mahler, he tells me about his newest inspiration: Rafael Nadal. "I've become a huge tennis fan over the last two or three years, and I'm a big Nadal supporter." He met Rafa last year, and gave him one of his recordings. "He was really touched, and that was when I learned that his grandfather, another Rafael Nadal, is a conductor, who, he said, 'knows everything about it'. It was sweet – I mean, how can you know everything about conducting?"

And what has Nézet-Séguin learned most from Nadal? "His intensity, the way he goes for every shot, is the way I like to conduct – to go for every note."